Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.22

Identify the effect on the graph of replacing $f(x)$ by $f(x) + k,$ $k \cdot f(x), f (kx),$ and $f(x + k)$ for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs. Experiment with cases and explain the effects on the graph using technology, where appropriate. Limit to linear functions. [Algebra I with Probability, 23]

Unpacked Content

Knowledge

Students know:
  • Linear relationships have input and output values that have an associated graph, including a y-intercept.
  • parallel lines have the same slope but different y-intercepts.

Skills

Students are able to:
  • Compare functions with the same slopes graphically while manipulating k values.
  • Explore functions with a calculator or graphing software to develop a relationshipbetween the coefficient on x and the slope.

Understanding

Students understand that:
  • Linear functions can shift based on factors other than the independent variable.
  • The shift of a function is not the same as the stretch of a function.

Vocabulary

  • Linear function
  • Slope
  • y-intercept
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